Definitions
What are factors?
Numbers you can multiply together to get another number.
Find the LCM of 9 and 4.
4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40...
9: 9, 18, 27, 36, 45...
The least common multiple is 36.
Find the GCF of 18 and 24.
The factors of 18 are: 1, 2, 3, 6, 9, 18
The factors of 24 are: 1, 2, 3, 4, 6, 8, 12, 24
The greatest common factor is 6.
Sara has 16 red flowers and 24 yellow flowers. She wants to make bouquets with the same number of each color flower in each bouquet. What is the greatest number of bouquets she can make?
The factors of 16 are: 1, 2, 4, 8, 16
The factors of 24 are: 1, 2, 3, 4, 6, 8, 12, 24
Then the greatest common factor is 8. Therefore she could make 8 bouquets.
Find the LCM of 2 and 5.
2: 2, 4, 6, 8, 10, 12, 14...
5: 5, 10, 15, 20, 25...
The Least Common Multiple is 10.
What is a common factor?
A number that is a factor of two or more numbers.
Find the LCM of 6 and 7.
6: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60...
7: 7, 14, 21, 28, 35, 42, 49, 56...
The least common multiple is 42
Find the GCF of 15 and 25.
The factors of 15 are: 1, 3, 5, 15
The factors of 25 are: 1, 5, 25
Then the greatest common factor is 5.
Peter has 18 oranges, 27 pears and 12 bananas. He wants to make fruit baskets with the same number of each fruit in each basket. What is the greatest number of fruit baskets he can make?
The factors of 12 are: 1, 2, 3, 4, 6, 12
The factors of 18 are: 1, 2, 3, 6, 9, 18
The factors of 27 are: 1, 3, 9, 27
Then the greatest common factor is 3. Therefore, the greatest number of fruit baskets he can make is 3.
Find the GCF of 32 and 11.
The factors of 11 are: 1, 11
The factors of 32 are: 1, 2, 4, 8, 16, 32
Then the greatest common factor is 1.
What is a multiple?
The result of multiplying a number by an integer.
Find the LCM of 9 and 10.
9: 9, 18, 27, 36, 45, 54, 63, 72, 81, 90...
10: 10, 20, 30, 40, 50, 60, 70, 80, 90...
The least common multiple is 90.
Find the GCF of 36 and 48.
The factors of 36 are: 1, 2, 3, 4, 6, 9, 12, 18, 36
The factors of 48 are: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
Then the greatest common factor is 12.
At the gym, Hillary swims every 6 days, runs every 4 days, and cycles every 16 days. If she did all three activities today, in how many days will she do all three activities again on the same day?
4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56...
6: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60...
16: 16, 32, 48...
She will do all three activities in 48 days.
Find the GCF of 27 and 18.
The factors of 18 are: 1, 2, 3, 6, 9, 18
The factors of 27 are: 1, 3, 9, 27
Then the greatest common factor is 9.
What does LCM stand for?
Least Common Multiple
Find the LCM of 2, 5 and 6.
2: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30...
5: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50...
6: 6, 12, 18, 24, 30, 36, 42...
The least common multiple is 30.
Find the GCF of 28, 35, and 45.
The factors of 28 are: 1, 2, 4, 7, 14, 28
The factors of 35 are: 1, 5, 7, 35
The factors of 45 are: 1, 3, 5, 9, 15, 45
Then the greatest common factor is 1.
Cups are sold 6 to a package and plates are sold 8 to a package. If you want to have the same number of each item for a party, what is the least number of packages of each you need to buy?
6: 6, 12, 18, 24, 30, 36, 42, 48, 54...
8: 8, 16, 24, 32, 40, 48, 56, 64, 72...
He needs to buy at least 24 of each, so 4 packages cups and 3 packages of plates.
Find the LCM of 4 and 9.
4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48...
9: 9, 18, 27, 36, 45...
The least common multiple is 36.
What does GCF stand for?
Greatest Common Factor
Find the LCM of 4, 5, and 6.
4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60...
5: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 60, 70, 80...
6: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66...
The least common multiple is 60.
Find the GCF of 32, 36, and 44.
The factors of 32 are: 1, 2, 4, 8, 16, 32
The factors of 36 are: 1, 2, 3, 4, 6, 9, 12, 18, 36
The factors of 44 are: 1, 2, 4, 11, 22, 44
Then the greatest common factor is 4.
I want to plant 45 sunflower plants, 81 corn plants and 63 tomato plants in my garden. If I put the same number of plants in each row and each row has only one type of plant, what is the greatest number of plants I can put in one row?
Factors of 45: 1, 3, 5, 9, 15, 45
Factors of 81: 1, 3, 9, 27, 81
Factors of 63: 1, 3, 7, 9, 21, 63
Therefore, I can put 9 in each row.
A radio station is having a promotion in which every 12th caller receives a free concert ticket, and every 15th caller receives a limo ride. Which caller will be the first one to win both?
12: 12, 24, 36, 48, 60, 72...
15: 15, 30, 45, 60, 75...
The 60th caller will win both.